This paper presents a finite element method for solving the neutron transport equation. The method is based on a discontinuous Galerkin approach, which has been shown to be strongly A-stable and of order 2k + 1. The method is applied to a two-dimensional neutron transport problem, where the spatial discretization is considered. The paper also provides error estimates and a superconvergence result for the method. The finite element method is shown to be effective in practice, and the results are validated through numerical examples. The method is applicable to polygonal domains and can be extended to general curved domains using curved isoparametric elements. The paper concludes with a discussion of the stability properties of the method and its potential for numerical solution of first-order hyperbolic problems.This paper presents a finite element method for solving the neutron transport equation. The method is based on a discontinuous Galerkin approach, which has been shown to be strongly A-stable and of order 2k + 1. The method is applied to a two-dimensional neutron transport problem, where the spatial discretization is considered. The paper also provides error estimates and a superconvergence result for the method. The finite element method is shown to be effective in practice, and the results are validated through numerical examples. The method is applicable to polygonal domains and can be extended to general curved domains using curved isoparametric elements. The paper concludes with a discussion of the stability properties of the method and its potential for numerical solution of first-order hyperbolic problems.